Exercise 7.23

Consider the following sentence: $[ ({Food} {\:\;{\Rightarrow}\:\;}{Party}) \lor ({Drinks} {\:\;{\Rightarrow}\:\;}{Party}) ] {\:\;{\Rightarrow}\:\;}[ ( {Food} \land {Drinks} ) {\:\;{\Rightarrow}\:\;}{Party}]\ .$

1. Determine, using enumeration, whether this sentence is valid, satisfiable (but not valid), or unsatisfiable.

2. Convert the left-hand and right-hand sides of the main implication into CNF, showing each step, and explain how the results confirm your answer to (a).

3. Prove your answer to (a) using resolution.